A Unified Analysis of Generalization and Sample Complexity for Semi-Supervised Domain Adaptation

Elif Vural; Huseyin Karaca

REVIEW 4 major objections 4 minor 79 references

A Unified Analysis of Generalization and Sample Complexity for Semi-Supervised Domain Adaptation

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper establishes a sample-complexity law for domain-adaptive neural networks: for both MMD-based and adversarial models of width $d$ and depth $L$, the labeled-source and total source and target samples needed to hold the target…

desk verdict Honest covering-number analysis with a useful α = O(√M_t) rule, but the load-bearing relatedness assumption can fail on simple label-shift and is never justified. read the letter →

arxiv 2507.22632 v1 pith:R67K7E7H submitted 2025-07-30 stat.ML cs.LG

Elif Vural , Huseyin Karaca This is my paper · ORCID

classification stat.MLcs.LG MSC 68Q3268T0768T05

keywords domainadaptationsemi-supervisedlearninggeneralizationboundssamplecomplexitymaximummeandiscrepancyadversarialcoveringnumbersdeepneuralnetworks

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out a unified theory of generalization for domain alignment algorithms: methods that map source and target data into a shared feature space through learned transformations and train a single classifier there, in the semi-supervised regime where target labels are scarce. Its central quantitative claim is a scaling law for deep domain-adaptive networks: whether alignment is enforced by maximum mean discrepancy or by an adversarial discriminator, the number of labeled source samples and the total number of source and target samples needed to keep the target generalization gap at $O(\epsilon)$ is $O((d^2 L \log(L/\epsilon) + d^2 L^2 \log d)/\epsilon^2)$, i.e., quadratic in the network width $d$ and depth $L$ up to log factors. It further claims that the weight $\alpha$ of the target classification loss should shrink as $\alpha = O(\sqrt{M_t})$ with the number of labeled target samples, turning label scarcity into an automatic downweighting of the target term. A reader would care because this converts a heuristic design choice, namely how large a domain-adaptive network can be trained from a given label budget, into a testable quantitative law, and it is the first explicit sample-complexity characterization for this family of models.

What carries the argument

The engine of the argument is a covering-number analysis of the function classes induced by the network: the feature transformation classes $\mathcal{F}^s, \mathcal{F}^t$ that map each domain into the shared space, and the composite hypothesis classes $\mathcal{H} \circ \mathcal{F}^s$, $\mathcal{H} \circ \mathcal{F}^t$ formed by a transformation followed by the classifier, plus, in the adversarial case, the classes $\mathcal{V}^s = \mathcal{D} \circ \mathcal{F}^s$ and $\mathcal{V}^t = \mathcal{D} \circ \mathcal{F}^t$ of discriminator-and-feature-extractor compositions; a covering number of a function class is the minimum number of small balls needed to cover it, so it measures how complex the class is. Lemma 7 and Lemma 8 build explicit parameter-grid covers of these classes, yielding the growth rate $O((L/\epsilon)^{d^2 L} (c d)^{d^2 L^2})$ for width $d$ and depth $L$ (Corollary 1). Lemma 2 then controls the deviation between expected and empirical weighted losses by a union bound over these covers, while Lemma 4 (MMD) and Lemma 9 (adversarial) control the deviation between the true and empirical domain discrepancy via Yurinskii's exponential inequality and Hoeffding's inequality, respectively; Theorem 2 combines the pieces for the MMD case, and Theorems 3 and 4 turn the union-bound probability expression into sample-complexity statements by choosing sample sizes so that each failure term stays bounded.

What would settle it

Take a digit dataset and a target domain with the same input distribution but permuted class labels, so the marginal features can be aligned to near-zero MMD or discriminator confusion while the classification-loss gap stays large, and measure the ratio $|L^s - L^t|/D(f^s, f^t)$ across hypotheses; if that ratio can be driven arbitrarily large while the alignment loss is small, Assumption 1 or 12 fails and the constant $R$ in the bounds degenerates. Conversely, on benchmarks where the ratio stays bounded, the predicted quadratic growth of required sample sizes with depth and width, and the $\alpha \propto \sqrt{M_t}$ schedule, are directly checkable by fitting the minimum $M_s$ and $N_s$ needed to hold a fixed target accuracy.

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Extended reading notes

Core claim

The paper's central claim, stated on its own terms, is a sample-complexity law for domain-adaptive neural networks. For an MMD-based network of width $d$ and depth $L$ (Theorem 3), keeping the expected target loss within $O(\epsilon)$ of the empirical weighted loss plus the empirical alignment term requires the number $M_s$ of labeled source samples and the total numbers $N_s, N_t$ of source and target samples all to be of order $O((d^2 L \log(L/\epsilon) + d^2 L^2 \log d)/\epsilon^2)$, with the target-loss weight set to $\alpha = O((M_t \epsilon^2/(d^2 L \log(L/\epsilon) + d^2 L^2 \log d))^{1/2})$: the $O(\sqrt{M_t})$ scaling when the network size is held fixed. For adversarial networks (Theorem 4) the same law holds for $M_s$, while the unlabeled totals become $O((d^2 (L+K) \log((L+K)/\epsilon) + d^2 (L+K)^2 \log d)/\epsilon^2)$, with $L+K$ the combined depth of the feature extractor and the domain discriminator. The paper also claims, at the general level of Theorem 1 and Theorem 2, that for any domain alignment algorithm the expected target loss is bounded by the empirical weighted loss plus $(1-\alpha)$ times the discrepancy between the aligned domains, with failure probability decaying exponentially in the labeled sample sizes once the covering numbers of the relevant function classes are accounted for.

Load-bearing premise

The load-bearing premise is Assumption 1 (Eq. 3): a finite constant $R$ must exist such that, for every allowed transformation pair and hypothesis, the gap between the expected source loss and the expected target loss is at most $R$ times the distribution discrepancy between the aligned domains, and in the adversarial setting this is re-posed as Assumption 12 (Eq. 37), where the paper itself notes that the learned discriminator must be sufficiently well trained to certify poor alignment whenever the loss gap is large; if that relatedness condition fails, the target loss is no longer controlled by the source loss plus the discrepancy term, and Theorems 1 through 4 collapse.

Editorial extensions

If this is right

Both MMD-based and adversarial domain-adaptive networks of width $d$ and depth $L$ require only on the order of $(d^2 L \log(L/\epsilon) + d^2 L^2 \log d)/\epsilon^2$ labeled source samples and total source and target samples to keep the target generalization gap at $O(\epsilon)$, meaning sample needs grow quadratically in depth and width up to log factors.
In the adversarial setting the unlabeled-sample requirement is governed by the combined depth $L+K$ of the feature extractor plus domain discriminator, so a larger discriminator taxes the data budget just as a deeper classifier does.
Scaling the target-loss weight as $\alpha = O(\sqrt{M_t})$ avoids overfitting the model to a handful of target labels, so scarcity of labeled target data is handled by downweighting the target term rather than by acquiring more labels.
The bounds hold in terms of the empirical weighted loss and the empirical discrepancy computed on the aligned data, so they give a directly computable certificate of target performance rather than an abstract asymptotic statement.
Because the MMD and adversarial settings share the same scaling law and the same proof skeleton, the quadratic depth-width dependence appears to be a property of the alignment architecture itself rather than of the particular discrepancy objective.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A practical corollary the authors leave implicit is a budgeting rule: if the quadratic law is accurate, cutting the labeled data roughly in half should be compensated by shrinking depth or width by a factor near $\sqrt{2}$, a prediction that could be checked on standard benchmarks without any new theory.
The covering-number route suggests the same machinery can be pushed to other alignment objectives, such as Wasserstein or correlation-alignment losses and norm-regularized feature extractors, where the depth exponent might differ; whether the quadratic-in-depth law is universal or an artifact of unconstrained parameterizations is a direct follow-up.
The paper itself notes in Remark 6 that norm constraints on weight matrices are expected to tighten the bounds, so a concrete test is whether spectrally regularized domain-adaptive networks beat the unconstrained quadratic sample law in practice.
Since the relatedness premise ties the certificate to loss-relevance of alignment, empirically estimating the constant $R$ on a benchmark would tell practitioners whether the quadratic law is the right budgeting tool there, especially under label shift with matched marginals.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First: the covering-number analysis is real, and the α = O(√M_t) rule is a clean takeaway. But the paper's headline sample-complexity result only holds if one accepts Assumption 1, and that assumption is doing far more work than the paper admits. It essentially says the loss gap is bounded by a feature-mean distance, which fails for straightforward label shift. So the practical scope is narrower than the title suggests.

What's genuine: For MMD-based and adversarial networks, the paper gets explicit O(d^2 L^2 / ε^2) bounds on Ms, Ns, Nt, with a corresponding α = O(√M_t) target-loss weight. The covering-number estimates for the function classes induced by these architectures are the real contribution; the appendices are thorough and standard. I believe those derivations are correct, and the derivation of the α rule from the exponential term is not circular. They also clearly distinguish their setting from same-space DA and transfer learning.

Where it's soft: Assumption 1 (Eq. 3) and its adversarial twin Assumption 12 (Eq. 37) are assumed, not derived. The stress-test example is legitimate: constant embeddings give D=0 while the loss gap can be nonzero under label shift, so no finite R exists without additional constraints. The paper doesn't give a class of distributions where the assumption holds, nor any empirical check. For adversarial, Assumption 12 additionally depends on the learned discriminator being strong enough, but they don't prove the min-max game yields that. The experiments are supportive but they fit curves to data without error bars, so they read as illustrative rather than confirmatory. And the stray inserted passage in Section 5.1 (Figure 5.7, DASGA, etc.) is clearly copied from elsewhere and has to go.

Bottom line: This is a serious theoretical paper with detailed proofs, and it deserves a careful referee. But the referee should push hard on the assumptions. If Assumption 1 cannot be weakened or verified for some non-trivial family, the contribution is mostly a conditional analysis. I'd like to see them characterize when Assumption 1 holds, or at least give an example of a real distribution family that satisfies it. As it stands, the claim is really 'sample complexity under a strong relatedness condition.' My recommendation: send it to review, but expect major revisions on the assumption handling.

Referee Report

4 major / 4 minor

Summary. The paper develops a theoretical framework for semi-supervised domain adaptation in which source and target feature transformations and a shared classifier are learned jointly by minimizing a weighted empirical classification loss together with a distribution discrepancy. Section 2 states a general bound (Theorem 1) on the expected target loss in terms of the empirical weighted loss and the true discrepancy, under an assumed Lipschitz-type relation between the loss gap and the discrepancy (Assumption 1). Theorem 2 replaces the true MMD by its empirical estimate using covering-number and concentration arguments. Section 3 specializes these results to MMD-based and adversarial deep networks, deriving covering-number bounds for the relevant function classes (Lemmas 7-8, Corollary 1) and sample-complexity statements (Theorems 3-4) of the form O((d^2 L log(L/epsilon) + d^2 L^2 log d)/epsilon^2), with the target-loss weight recommended to scale as alpha = O(sqrt(M_t)). Section 5 reports synthetic and image experiments whose fitted curves follow the predicted O(L^2), O(d^2), and O(sqrt(M_t)) trends.

Significance. If the two relatedness assumptions were justified, this would be a substantial contribution: it would give one of the first explicit width/depth sample-complexity bounds for alignment-based domain-adaptive neural networks, and it would provide a concrete, testable prescription for the target-loss weight. The modular proof strategy is a real strength: Lemma 2 combines Hoeffding bounds with covering numbers, Lemma 4 uses Yurinskii's inequality for uniform MMD deviation, and the covering-number analysis for multi-layer kernel feature maps in Lemmas 7-8 and Corollary 1 is nontrivial and carefully worked out. The experimental section is also commendable for attempting to verify the scaling laws in both shallow and deep settings. However, the headline claims are conditional on Assumption 1 (Eq. 3) and Assumption 12 (Eq. 37), and those assumptions are neither derived from data properties nor verified empirically; for label-shift settings they can fail while all measurable premises of the theorems hold. The contribution is therefore best read as a conditional analysis of alignment-based DA rather than as an established sample-complexity theory.

major comments (4)

[Section 2.2, Eq. (3)] Assumption 1 is not a mild relatedness condition; it is the load-bearing mechanism of the entire paper. With D chosen as the first-moment MMD in Eq. (7), take f_s and f_t to be zero-weight constant maps (admissible under the parameter bounds of Assumption 5), source labels Y = sign(x_1), target labels Y = -sign(x_1), and h(x) = x. Then D(f_s, f_t) = 0 while |L_s(f_s,h) - L_t(f_t,h)| = 1, so no finite R exists. This shows that the assumption excludes label shift, which is one of the standard domain-adaptation challenges named in the Introduction. Since Lemma 1 and Theorems 1-4 all use inequality (3) directly, the claimed O(d^2 L^2/epsilon^2) sample complexity holds only for problems in which the label-shift part of the transfer has already been assumed away.
[Section 3.2, Eq. (37)] Assumption 12 has the same structural problem as Assumption 1 and an additional algorithmic dependence. The scalar distance D_Delta(f_s,f_t) is a mean difference of the discriminator outputs, so it carries only first-moment information about the discriminator's view of the features. Moreover, the inequality (37) is assumed only for the discriminator Delta returned by the min-max optimization in Eq. (31). Lemma 9 provides uniform concentration for sup_{f_s,f_t,Delta} |D_Delta - hat-D_Delta| over all Delta in D, but it does not prove that the particular Delta selected by the algorithm certifies inequality (37). The proof of Theorem 4 in Appendix M invokes Assumption 12 at the first line without any derivation of this certification property. The adversarial result is therefore subject to both the label-shift concern and an unverified algorithmic condition.
[Theorems 3 and 4, Eqs. (29) and (39)] The stated sample-complexity rates quote only O(d^2 L^2/epsilon^2) and hide the constants R and R_A. Since the target-loss bound contains the terms (1-alpha) R hat-D and (1-alpha) R epsilon (and the adversarial analogue), the value of R multiplies both the empirical discrepancy and the accuracy parameter. If R grows with d or L, as is possible when the loss gap and the first-moment discrepancy are not tightly coupled, the R-dependent constants could dominate the quoted scaling. The paper should either prove an explicit upper bound on R and R_A in terms of the data and network constants, or state explicitly that all scaling statements are modulo these assumption constants.
[Section 5] The experiments do not provide evidence for Assumptions 1 and 12. Figures 5, 7-13 fit the predicted rates O(1/sqrt(M_t)), O(L^2), and O(d^2) to target accuracy or required sample sizes, but they do not measure the discrepancies D or D_Delta, do not estimate R or R_A, and do not test inequality (3) or (37). A meaningful empirical check of the conditional claim would require either a distribution class for which R is known to be finite, or a diagnostic that directly compares the loss gap with the discrepancy on held-out data. Without such a check, the experiments support only the concentration-rate structure of the bounds, not the relatedness assumptions on which the main theorems rest.

minor comments (4)

[Section 3, paragraph after Theorem 3] The text calls epsilon 'a probability constant'; in Eq. (29) epsilon is the accuracy parameter that controls the generalization gap. This terminology should be corrected to avoid confusion.
[Section 4, Remark 5] Remark 5 states that the alpha = O(sqrt(M_t)) choice handles target-label scarcity 'independently of the complexity of the target function class', but the displayed alpha bound in Theorems 3 and 4 contains d^2 L log(L/epsilon) + d^2 L^2 log d in the denominator. The remark should be reworded to match the formula.
[Section 5.1, Figures 5, 7] The experimental plots show fitted dashed curves but no confidence intervals or repetitions over multiple random seeds; reporting variability would make the support for the claimed scaling laws more convincing.
[Figures 2 and 3 and Section 5.1] The manuscript contains LaTeX-editor artifacts such as 'Font size: 28 in latexit' in the figure captions and internal labels 'Figure 5.7/5.8' that should be cleaned before publication.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the sample-complexity bounds and alpha scaling follow from concentration and covering-number arguments, with only a non-load-bearing self-citation.

full rationale

The paper's central derivation is self-contained. Theorem 1 combines Lemma 1 (Assumption 1 plus weighted-loss decomposition) with Lemma 2 (Hoeffding/covering-number uniform deviation); Theorems 2-4 chain union bounds and explicit covering-number estimates proved in Appendices F-M. The claimed O(d^2 L log(L/eps)+d^2 L^2 log d)/eps^2 sample complexity is obtained by setting the exponents in (83) to remain bounded, not by fitting constants to data. Likewise alpha=O(sqrt M_t) is read off from the exponential exp(-M_t eps^2/alpha^2) in (5)/(38) so that the probability term stays fixed; this is a derived scaling rule, not an input imposed to produce the conclusion. Assumption 1 (Eq. 3) is an explicitly stated Lipschitz-type relatedness condition, not a hidden restatement of the theorem; the bound is conditional on it, and the paper does not claim to derive R or to verify Eq. 3 from the optimization problem. A reviewer could argue Eq. 3 is too strong or fails under label shift with matched feature means, but that is an assumption-validity/correctness concern, not circularity under the stated review rules. The only self-citation is [49] for the groundwork of Section 2.2, but Lemma 1, Lemma 2, and Theorem 1 are proven in the present manuscript, so the citation is not load-bearing. The experiments fit theoretical-rate curves to data for visual comparison, but the theoretical statements do not depend on those fits. Overall, the derivation chain does not reduce to its inputs; score 1 reflects the harmless self-citation.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The theorems take as inputs: a Lipschitz-type relationship between the loss gap and the domain discrepancy (Assumptions 1 and 12); Bernstein-like moment bounds on mapped features (Assumption 3); compactness and boundedness of function classes and network parameters (Assumptions 4-9); and standard concentration inequalities. None of these constants are fitted to data in the theory, but they are unverified existence assumptions; the empirical section later fits rates to data to illustrate the bounds. No new physical or mathematical entities are introduced.

free parameters (5)

R (Assumption 1 relatedness constant)
Assumed finite in Eq. (3); no value, bound, or estimation procedure is given, and it appears in every main bound.
sigma_s, sigma_t, C_s, C_t (moment constants)
Assumption 3 postulates finite variance and Bernstein-like moment growth; these constants set the exponential rates as(N_s, eps) and at(N_t, eps) in Lemmas 3-4 and Theorem 2.
RA (adversarial relatedness constant)
Assumption 12, Eq. (37); same role as R for the adversarial setting; existence assumed without construction.
Boundedness and Lipschitz constants (A_x, A_Theta, L_K, L_eta, A_eta, C_eta, A_l, L_l, C_D)
Assumptions 5-11; they define the compact hypothesis classes and enter the covering-number exponents; values are not estimated.
alpha (target loss weight)
Algorithm hyperparameter chosen by the practitioner; the theory recommends alpha = O(sqrt(M_t)) and experiments grid-search it, but it is not fitted inside the derivation.

assumptions (7)

domain assumption Assumption 1: |Ls(f_s,h) - Lt(f_t,h)| <= R D(f_s,f_t) for all f_s, f_t, h
Introduced in Eq. (3) before Lemma 1; it is the load-bearing bridge from source to target loss and is never verified.
domain assumption Assumption 3: finite variance and k-th moment bounds of order O(k! sigma^2 C^(k-2)) for mapped features
Eqs. (9)-(10) enable Yurinskii's exponential inequality; existence of sigma_s, sigma_t, C_s, C_t is assumed.
standard math Assumption 4: compactness of F_s and F_t under sup metrics
Needed for covering-number arguments; follows from boundedness assumptions later.
domain assumption Assumptions 5-8: bounded inputs and weights, Lipschitz kernels and activations, bounded activations
Section 3.1; these guarantee compactness and supply the covering-number bounds in Lemmas 6-8.
domain assumption Assumption 9: domain discriminator output is bounded by C_D
Section 3.2; used in Hoeffding concentration in Lemma 9; usually satisfied by sigmoid or softmax outputs.
domain assumption Assumption 12: |Ls(f_s,h) - Lt(f_t,h)| <= RA D_Delta(f_s,f_t)
Eq. (37); adversarial counterpart of Assumption 1, required to transfer the bound to the target loss.
standard math Hoeffding's inequality, union bound, Yurinskii's exponential inequality, Riesz representation theorem
Used in Lemmas 2, 3, 4 and Appendix D; classical results.

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Cite this review

Pith. "Pith review of A Unified Analysis of Generalization and Sample Complexity for Semi-Supervised Domain Adaptation." pith.science (2026). https://pith.science/paper/R67K7E7H

@misc{pith2026250722632,
  author       = {Pith},
  title        = {Pith review of: A Unified Analysis of Generalization and Sample Complexity for Semi-Supervised Domain Adaptation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R67K7E7H}},
  note         = {Machine review of arXiv:2507.22632}
}

read the original abstract

Domain adaptation seeks to leverage the abundant label information in a source domain to improve classification performance in a target domain with limited labels. While the field has seen extensive methodological development, its theoretical foundations remain relatively underexplored. Most existing theoretical analyses focus on simplified settings where the source and target domains share the same input space and relate target-domain performance to measures of domain discrepancy. Although insightful, these analyses may not fully capture the behavior of modern approaches that align domains into a shared space via feature transformations. In this paper, we present a comprehensive theoretical study of domain adaptation algorithms based on domain alignment. We consider the joint learning of domain-aligning feature transformations and a shared classifier in a semi-supervised setting. We first derive generalization bounds in a broad setting, in terms of covering numbers of the relevant function classes. We then extend our analysis to characterize the sample complexity of domain-adaptive neural networks employing maximum mean discrepancy (MMD) or adversarial objectives. Our results rely on a rigorous analysis of the covering numbers of these architectures. We show that, for both MMD-based and adversarial models, the sample complexity admits an upper bound that scales quadratically with network depth and width. Furthermore, our analysis suggests that in semi-supervised settings, robustness to limited labeled target data can be achieved by scaling the target loss proportionally to the square root of the number of labeled target samples. Experimental evaluation in both shallow and deep settings lends support to our theoretical findings.

Figures

Figures reproduced from arXiv: 2507.22632 by the authors.

**Figure 2.** Illustration of MMD-based domain adaptation networks [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

**Figure 3.** Illustration of adversarial domain adaptation networks [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: Illustration of Assumption 12. Red and blue colors represent two different [PITH_FULL_IMAGE:figures/full_fig_p023_4.png]

**Figure 5.** Figure 5: Variation of the target error on synthetical data with (a) Number of labeled [PITH_FULL_IMAGE:figures/full_fig_p031_5.png]

**Figure 5.7.** Figure 5.7: Sample images from the MIT-CBCL face data set for three different subj t[72]Lftt tiddltd ihtt tidd Figure 6: Sample images from the MIT-CBCL face data set for four different subjects, [PITH_FULL_IMAGE:figures/full_fig_p032_5_7.png]

**Figure 5.8.** Figure 5.8: Misclassification rates obtained with the proposed SDA and reference methods. Source domain: Pose 1, Target domain: Pose 2 of a total of 3240 synthetic face images belonging to 10 subjects. The images of each [PITH_FULL_IMAGE:figures/full_fig_p032_5_8.png]

**Figure 8.** Figure 8: Sample complexity of labeled samples (Ms) and all samples (Ns) with respect to the depth L of MMD-based domain adaptation networks. Left panels (a),(c): Variation of target accuracy with L. Right panels (b),(d): Variation of the number of samples (Ms, Ns) required for…

**Figure 9.** Figure 9: Sample complexity of labeled samples (Ms) with respect to the width d of MMD-based domain adaptation networks. (a) Variation of target accuracy with d. (b) Variation of the number of samples (Ms) required for attaining a desired target accuracy level with d. We also re…

**Figure 10.** Figure 10: (a) Variation of target accuracy with target loss weight parameter [PITH_FULL_IMAGE:figures/full_fig_p036_10.png]

**Figure 11.** Figure 11: Sample complexity of labeled samples (Ms) and all samples (Ns) with respect to the depth L of adversarial domain adaptation networks. Left panels (a),(c): Variation of target accuracy with L. Right panels (b),(d): Variation of the number of samples (Ms, Ns) required f…

**Figure 12.** Figure 12: Sample complexity of labeled samples (Ms) and all samples (Ns) with respect to the width d of adversarial domain adaptation networks. Left panels (a),(c): Variation of target accuracy with d. Right panels (b),(d): Variation of the number of samples (Ms, Ns) required f…

**Figure 13.** Figure 13: (a) Variation of target accuracy with target loss weight parameter [PITH_FULL_IMAGE:figures/full_fig_p039_13.png]

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